유리식의 연산Rational Expressions · 문제집Worksheet

$\dfrac{x^2 - 9}{x^2 + 5x + 6}$을 약분하고 제외 조건을 밝혀라.

Simplify $\dfrac{x^2 - 9}{x^2 + 5x + 6}$ and state the exclusions.

$\dfrac{x^2 - 4}{x + 1} \times \dfrac{x + 1}{x - 2}$를 간단히 하여라.

Simplify $\dfrac{x^2 - 4}{x + 1} \times \dfrac{x + 1}{x - 2}$.

$\dfrac{x + 3}{x} \div \dfrac{x^2 - 9}{x^2}$을 간단히 하여라.

Simplify $\dfrac{x + 3}{x} \div \dfrac{x^2 - 9}{x^2}$.

$\dfrac{2}{x - 1} + \dfrac{3}{x + 2}$를 한 분수로 나타내어라.

Combine $\dfrac{2}{x - 1} + \dfrac{3}{x + 2}$ into one fraction.

$\dfrac{1}{x^2 - x} + \dfrac{1}{x^2 - 1}$을 한 분수로 나타내어라.

Combine $\dfrac{1}{x^2 - x} + \dfrac{1}{x^2 - 1}$ into one fraction.

$\dfrac{3}{x - 2} - \dfrac{x + 1}{x^2 - 4}$를 간단히 하여라.

Simplify $\dfrac{3}{x - 2} - \dfrac{x + 1}{x^2 - 4}$.

번분수 $\dfrac{1 + \dfrac{2}{x}}{1 - \dfrac{4}{x^2}}$를 간단히 하여라.

Simplify the complex fraction $\dfrac{1 + \dfrac{2}{x}}{1 - \dfrac{4}{x^2}}$.

$\dfrac{x + 2}{x + 3}$에서 $x$끼리 "약분"하여 $\dfrac{2}{3}$이라 하면 왜 틀리는지 설명하여라.

Explain why "cancelling" the $x$'s in $\dfrac{x + 2}{x + 3}$ to get $\dfrac{2}{3}$ is wrong.

(1) $\dfrac{1}{x(x + 1)} = \dfrac{1}{x} - \dfrac{1}{x + 1}$임을 확인하여라.

(2) 이를 이용해 $\dfrac{1}{1 \cdot 2} + \dfrac{1}{2 \cdot 3} + \cdots + \dfrac{1}{9 \cdot 10}$을 구하여라.

(1) Verify $\dfrac{1}{x(x + 1)} = \dfrac{1}{x} - \dfrac{1}{x + 1}$.

(2) Use it to evaluate $\dfrac{1}{1 \cdot 2} + \dfrac{1}{2 \cdot 3} + \cdots + \dfrac{1}{9 \cdot 10}$.

$\left(\dfrac{x}{x - 1} - 1\right) \div \dfrac{1}{x^2 - 1}$을 간단히 하여라.

Simplify $\left(\dfrac{x}{x - 1} - 1\right) \div \dfrac{1}{x^2 - 1}$.

항등식 $\dfrac{5x + 1}{(x - 1)(x + 2)} = \dfrac{a}{x - 1} + \dfrac{b}{x + 2}$를 만족하는 상수 $a$, $b$를 구하여라.

Find constants $a$, $b$ satisfying the identity $\dfrac{5x + 1}{(x - 1)(x + 2)} = \dfrac{a}{x - 1} + \dfrac{b}{x + 2}$.

연분수 $1 + \cfrac{1}{1 + \cfrac{1}{1 + \cfrac{1}{x}}}$를 하나의 유리식으로 정리하여라.

Simplify the continued fraction $1 + \cfrac{1}{1 + \cfrac{1}{1 + \cfrac{1}{x}}}$ into a single rational expression.

$x + \dfrac{1}{x} = 3$일 때, $x^2 + \dfrac{1}{x^2}$과 $x^3 + \dfrac{1}{x^3}$의 값을 구하여라.

Given $x + \dfrac{1}{x} = 3$, find $x^2 + \dfrac{1}{x^2}$ and $x^3 + \dfrac{1}{x^3}$.